پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 685 |
| تعداد مقالات | 9,958 |
| تعداد مشاهده مقاله | 70,841,116 |
| تعداد دریافت فایل اصل مقاله | 62,333,495 |
Some results of domination on the discrete topological graph with its inverse | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 14، شماره 6، شهریور 2023، صفحه 23-29 اصل مقاله (615.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6849 | ||
| نویسندگان | ||
| Zainab N. Jwair؛ Mohammed A. Abdlhusein* | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 22 اسفند 1400، تاریخ بازنگری: 16 فروردین 1401، تاریخ پذیرش: 29 اردیبهشت 1401 | ||
| چکیده | ||
| Let $G_{\tau }=\left(V,\ E\right)$ be a topological graph which is a finite, simple, undirected, connected graph without isolated vertices. In this paper, several bounds and domination parameters are studied and applied to it: bi-domination, doubly connected bi-domination and pitchfork domination. The dominating set and domination number with its inverse for all these types are calculated. Also, some figures from the topological graph are introduced. | ||
| کلیدواژهها | ||
| Topological graph؛ discrete topology؛ dominating set؛ domination number | ||
| مراجع | ||
|
[1] M.A. Abdlhusein, New approach in graph domination, Ph. D. Thesis, University of Baghdad, 2020. [2] M.A. Abdlhusein, Doubly connected bi-domination in graphs, Discrete Math. Algorithms Appl. 13 (2021), no. 2, 2150009. [3] M.A. Abdlhusein, Stability of inverse pitchfork domination, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 1, 1009–1016. [4] M.A. Abdlhusein, Applying the (1, 2)-pitchfork domination and its inverse on some special graphs, Bol. Soc. Paran. Mat. Accepted to appear, 2021. [5] M.A. Abdlhusein and M.N. Al-Harere, Total pitchfork domination and its inverse in graphs, Discrete Math. Algorithms Appl. 13 (2021), no. 4, 2150038. [6] M.A. Abdlhusein and M.N. Al-Harere, New parameter of inverse domination in graphs, Indian J. Pure Appl. Math. 52 (2021), no. 1, 281–288. [7] M.A. Abdlhusein and M.N. Al-Harere, Doubly connected pitchfork domination and it’s inverse in graphs, TWMS J. Appl. and Eng. Math. 12 (2022), no. 1, 82–91. [8] M.A. Abdlhusein and M.N. Al-Harere, Pitchfork domination and it’s inverse for corona and join operations in graphs, Proc. Int. Math. Sci. 1 (2019), no. 2, 51–55. [9] M.A. Abdlhusein and M.N. Al-Harere, Pitchfork domination and its inverse for complement graphs, Proc. Inst. Appl. Math. 9 (2020), no. 1, 13–17. [10] M.A. Abdlhusein and M.N. Al-Harere, Some modified types of pitchfork domination and its inverse, Bol. Soc. Paran. Mat. 40 (2022), 1–9. [11] M.A. Abdlhusein and S.J. Radhi, The arrow edge domination in graphs, Int. J. Nonlinear Anal. Appl, 13 (2022), no. 2, 591–597. [12] Z.H. Abdulhasan and M.A. Abdlhusein, Triple effect domination in graphs, AIP Conf. Proc. 2022, 060013. [13] Z.H. Abdulhasan and M.A. Abdlhusein, An inverse triple effect domination in graphs, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 913–919. [14] Z.H. Abdulhasan and M.A. Abdlhusein, Stability and some results of triple effect domination, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 4, 349-358. [15] M.N. Al-Harere and M.A. Abdlhusein, Pitchfork domination in graphs, Discrete Math. Algorithms Appl. 12 (2020), no. 2, 2050025. [16] M.N. Al-Harere and A.T. Breesam, Further results on bi-domination in graphs, AIP Conf. Proc. 2096 (2019), no. 1, pp. 20013. [17] L.K. Alzaki, M.A. Abdlhusein and A. K. Yousif, Stability of (1, 2)-total pitchfork domination, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 265–274. [18] T.W. Haynes, S.T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, INC. New York, 1998. [19] M.K. Idan and M.A. Abdlhusein, Some properties of discrete topological graph, J. Phys.: Conf. Series, accepted to appear, 2022. [20] M.K. Idan and M.A. Abdlhusein, Different types of dominating sets of the discrete topological graph, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 1, 101-108. [21] M.K. Idan and M.A. Abdlhusein, Some dominating results of the join and corona operations between discrete topological graphs, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 5, 235-242. [22] M.K. Idan and M.A. Abdlhusein, Topological space generated by edges neighborhoods of topological graph, Preprint, 2022. [23] M.K. Idan and M.A. Abdlhusein, Topological space generated by vertices neighborhoods of topological graph, Preprint, 2022. [24] Z.N. Jwair and M.A. Abdlhusein, Applying some dominating parameters on the topological graph, J. Phys.: Conf. Ser., accepted to appear, 2022. [25] Z.N. Jwair and M.A. Abdlhusein, Some dominating results of the topological graph, Int. J. Nonlinear Anal. Appl. In press, 2022, Doi: 10.22075/IJNAA.2022.6404. [26] Z.N. Jwair and M.A. Abdlhusein, Constructing new topological graph with several properties, Iraqi J. Sci., to appear, 2022. [27] Z.N. Jwair and M.A. Abdlhusein, The neighborhood topology converted from the undirected graphs, Preprint, 2022. [28] Z.N. Jwair and M.A. Abdlhusein, Several parameters of domination and inverse domination of discrete topological graphs, Preprint, 2022. [29] V.R. Kulli and S.C. Sigarkanti, Inverse domination in graphs, Nat. Acad. Sci. Lett. 14 (1991), 473–475. [30] S.J. Radhi, M.A. Abdlhusein and A.E. Hashoosh, The arrow domination in graphs, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 1, 473–480. [31] S.J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, Some modified types of arrow domination, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 1451–1461. [32] M.S. Rahman, Basic graph theory, Springer, India, 2017. [33] S. Willard, General topology, Dover Publications, INC. Mineola, New York, 2012. | ||
|
آمار تعداد مشاهده مقاله: 16,967 تعداد دریافت فایل اصل مقاله: 10,592 |
||